Mathematics · Quantitative Aptitude

Geometry of Triangles and Angles

846 Questions

Triangle and angle geometry covers angle sums, properties of equilateral shapes, and right triangles. These principles form the basis of advanced quantitative aptitude sections. Practicing spatial problems helps secure points in exams.

Triangle angle sumsPythagorean theoremProperties of equilateral trianglesComplementary and supplementary anglesRight triangle formulas

Geometry of Triangles and Angles Questions

Multiple choice

What is the measure of an angle that is three times the size of its supplementary angle?

  1. 45°

  2. 60°

  3. 75°

  4. 90°
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the measure of the supplementary angle. Then, the measure of the angle that is three times the size of its supplementary angle is 3x. Since the sum of the two angles is 180 degrees, we have x + 3x = 180. Solving for x, we get x = 45. Therefore, the measure of the angle that is three times the size of its supplementary angle is 3x = 3 * 45 = 135 degrees.

Multiple choice

In a triangle, the measure of one angle is twice the measure of the second angle, and the measure of the third angle is three times the measure of the second angle. What is the measure of the largest angle?

  1. 60°

  2. 90°

  3. 120°

  4. 150°
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the measure of the second angle. Then, the measure of the first angle is 2x and the measure of the third angle is 3x. Since the sum of the angles in a triangle is 180 degrees, we have x + 2x + 3x = 180. Solving for x, we get x = 30. Therefore, the measure of the largest angle, which is the third angle, is 3x = 3 * 30 = 90 degrees.

Multiple choice

In a quadrilateral, the measure of one angle is 100°, the measure of the second angle is 120°, and the measure of the third angle is 140°. What is the measure of the fourth angle?

  1. 100°

  2. 120°

  3. 140°

  4. 160°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the angles in a quadrilateral is 360 degrees. Therefore, the measure of the fourth angle is 360 - 100 - 120 - 140 = 100 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse?

  1. Pythagorean Theorem

  2. Euler's Theorem

  3. Fermat's Last Theorem

  4. Goldbach's Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem, also known as Pythagoras' Theorem, is a fundamental theorem in geometry that establishes the relationship between the sides of a right triangle.

Multiple choice

What is the name of the theorem that states that the sum of the squares of two sides of a right triangle is equal to the square of the hypotenuse?

  1. Pythagorean theorem

  2. Euler's theorem

  3. Fermat's Last Theorem

  4. Goldbach conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean theorem is a fundamental theorem in geometry that states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a triangle is always 180 degrees?

  1. Pythagorean theorem

  2. Euler's theorem

  3. Fermat's Last Theorem

  4. Triangle sum theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The triangle sum theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Multiple choice

Which theorem states that the sum of the interior angles of a triangle is always (180^\circ)?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Law of Cosines
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Angle Sum Theorem states that the sum of the interior angles of a triangle is always (180^\circ).

Multiple choice

Which theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Law of Cosines
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Multiple choice

What is the relationship between binomial coefficients and Pascal's Triangle?

  1. The entries in Pascal's Triangle are equal to binomial coefficients.

  2. The entries in Pascal's Triangle are the sums of binomial coefficients.

  3. The entries in Pascal's Triangle are the differences of binomial coefficients.

  4. The entries in Pascal's Triangle are the products of binomial coefficients.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pascal's Triangle is a triangular array of binomial coefficients, where each entry is the sum of the two entries above it. The first row of Pascal's Triangle consists of 1, the second row consists of 1 and 1, and so on.

Multiple choice

What is the name of the famous trigonometric function that calculates the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle?

  1. Sine

  2. Cosine

  3. Tangent

  4. Cosecant
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sine function is a fundamental trigonometric function that calculates the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. It plays a crucial role in various mathematical and scientific applications.

Multiple choice

What is the name of the trigonometric function that calculates the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle?

  1. Sine

  2. Cosine

  3. Tangent

  4. Cosecant
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cosine function is a trigonometric function that calculates the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is widely used in various mathematical and scientific applications.

Multiple choice

What is the name of the trigonometric function that calculates the ratio of the length of the opposite side to the length of the adjacent side in a right triangle?

  1. Sine

  2. Cosine

  3. Tangent

  4. Cosecant
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The tangent function is a trigonometric function that calculates the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is widely used in various mathematical and scientific applications.

Multiple choice

What is the name of the trigonometric function that calculates the ratio of the length of the hypotenuse to the length of the opposite side in a right triangle?

  1. Sine

  2. Cosine

  3. Tangent

  4. Secant
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The secant function is a trigonometric function that calculates the ratio of the length of the hypotenuse to the length of the opposite side in a right triangle. It is widely used in various mathematical and scientific applications.

Multiple choice

Bhaskara I also developed a formula for the cosine of an angle, which is given by:

  1. $$cos(x) = rac{adjacent}{hypotenuse}$$
  2. $$cos(x) = rac{opposite}{hypotenuse}$$
  3. $$cos(x) = rac{opposite}{adjacent}$$
  4. $$cos(x) = rac{hypotenuse}{opposite}$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara I's formula for the cosine of an angle is $$cos(x) = rac{adjacent}{hypotenuse}$$, where x is the angle and adjacent and hypotenuse are the lengths of the adjacent and hypotenuse sides of the right triangle, respectively.

Multiple choice

What is the name of the mathematical theorem that states that the sum of the angles of a triangle is equal to 180 degrees?

  1. Pythagorean Theorem

  2. Pascal's Triangle

  3. Euler's Formula

  4. Angle Sum Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Angle Sum Theorem states that the sum of the angles of a triangle is equal to 180 degrees.